I contacted Martha Burns, who did a lot to promote the recordings of Craig Johnson in his final years. Here's what she said:

Good question. I looked in my plant apps and on the web. The nearest things to an explanation I could find was in Merriam-Webster's. I've attached a screenshot, since you may not subscribe. sticky laurel
noun: a buckbrush (Ceanothus velutinus) with gummy twigs and evergreen leaves
            Less encouraging, I found this list of twenty-five types of laurel. No stick, sticky, or gum-stick laurel there. https://homescopes.com/garden/types-of-laurel/
            I think the Merriam-Webster's reference is probably closest to what Craig was envisioning.

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And that makes sense to me, since I live in a house in the Sierra Foothills that's surrounded by buckbrush, a ceanothus with white flowers. It's pretty when it's in bloom, but it's noxious to people with allergies and it's a fire hazard when it dries out a bit. My stepson was allergic - every Spring was tough until he moved out of the house.